A number of observations
[1]}, [2]}, [3]}, [4]}, [5]}, [6]}, [7]}, [8]}, [9]}, [10]}, [11]}, [12]}, [13]}, [14]}, [15]}, [16]}, [17]}, [18]}, [19]}, [20]}, [21]}, [22]}, [23]}, [24]}, [25]}, [26]}, [27]}, [28]}, [29]}, [30]}, [31]}, [32]}, [33]}, [34]}, [35]}, [36]}, [37]}, [38]}, [39]}, [40]}, [41]}, [42]}, [43]}, [44]}, [45]}, [46]}, [47]}, [48]}, [49]}, [50]}, [51]} have indicated that the present universe is undergoing a phase of accelerated expansion, and
driven probably by a new form of energy with negative EoS parameter, commonly so-called DE [52]}. This energy has been interpreted in
various forms and widely studied in [53]}.
However, within General Relativity (GR) the DE models can suffer the coincidence problem, namely why the DM and DE energy densities are of the same
order today. This latter problem could be solved or even alleviated, by assuming the existence of a non-gravitational \(\bar{Q}\)  within the dark
sector, which gives rise to a continuous energy exchange from DE to DM or vice-versa. Currently, there are n't neither physical arguments nor
recent observations to exclude \(\bar{Q}\)  [54]}, [55]}, [56]}, [57]}. Moreover, due to the absence of a fundamental theory
to construct \(\bar{Q}\) , different ansatzes have been widely discussed in [54]}, [55]}, [56]}, [57]}, [62]}, [63]}.
So, It has been shown in some coupled DE scenarios that \(\bar{Q}\)  can affect the background evolution of the DM density perturbations and the expansion
history of the universe [6]}, [62]}, [63]}, [67]}, [68]}. Thus, \(\bar{Q}\)  and \(\mathrm {\omega _{DE}}\)  could very possibly introduce new features on
the evolution curves of the structure growth of the matter, on the linear matter power spectrum and on the amplitude of the CMB temperature power
spectrum at low and high multipoles, respectively [6]}, [63]}, [67]}, [68]}, [73]}.
